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Nehemiah, Yohanna
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An Enhanced Variational Iteration Method for Solving Ordinary and Partial Differential Equations Hassan, Araga; Adamu, M. Y.; Madaki, A. G.; Nehemiah, Yohanna; Cornelius, Michael; Nasir, U. M.
Journal of Multidisciplinary Science: MIKAILALSYS Vol 3 No 2 (2025): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v3i2.5317

Abstract

The Variational Iteration Method (VIM) has proven to be a powerful technique for solving both ordinary and partial differential equations. However, its reliance on Lagrange multipliers for each type of equation has posed significant limitations, complicating its application and reducing its efficiency. This study introduces a Modified Variational Iteration Method (MVIM) that eliminates the need for Lagrange multipliers, addressing these challenges. The MVIM reformulates the correctional functional, simplifying the solution process and enhancing computational efficiency. The method is applied to both linear and nonlinear ordinary and partial differential equations, demonstrating its ability to provide accurate and fast-converging solutions. Numerical examples show that the MVIM outperforms traditional VIM in terms of computational time and convergence speed, and compares favourably with other methods such as the Adomian Decomposition Method (ADM) and New Iteration Method (NIM). The results highlight the potential of MVIM as a versatile and efficient tool for solving complex differential equations in a variety of scientific and engineering applications.
A Semi-Analytical Method for Nonlinear System of Delay Differential Equation via Modified He’s Polynomial Nehemiah, Yohanna; Barde, Aminu; Madaki, A.; Cornelius, Michael
Journal of Multidisciplinary Science: MIKAILALSYS Vol 3 No 2 (2025): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v3i2.5319

Abstract

In this work, a simple technique based on the combination of sumudu transform and variational iteration method via Modified He’s polynomial is introduced to solve systems of non-linear delay differential equations. The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, the modified He’s polynomial takes care of the nonlinear terms and hence, making the method less stressful in terms of computations. Also, this technique reduces the complexity of calculating Lagrange’s multiplier values which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.
Co-Authors Barde, Aminu Cornelius, Michael Hassan, Araga M. Y. Adamu Madaki, A. Madaki, A. G. Nasir, U. M.